Electronic inclinometer

ABSTRACT

A sensor for an incination measuring device which comprises a capsule (3) part-filled with a conductive liquid. First to fourth electrodes (A-D) are disposed within the capsule in contact with the liquid. An electrical signal is applied between electrodes (C, D) and one then the other of electrodes (A, B), to derive a signal indicative of the degree of immersion of the electrode (A), and then the electrode (B) within the liquid. The ratio of these signals is related to the angle of inclination of the capsule about the reference axis (O) and relative to a first reference angle defined at the gap between the electrodes (A, B). The capsule (1) is also constructed to compensate for thermal effects, by forming the sides of the capsule so that they are responsive to pressure change within the capsule caused by thermal expansion of the contents of the capsule to expand the volume of the capsule, to keep the level of liquid therein constant.

This invention relates to a device and, more particularly, but notexclusively to a sensor for an electronic level or inclination gauge.

Optical levels, more commonly called spirit levels, are well known andprovide an optical indication of whether or not a surface is horizontal,based on the principle of an air bubble in a liquid-filled vial alwaysseeking the highest point in the vial, the vial being slightly curved sothat when at level, the bubble will always take up an equilibriumposition. Such bubble levels, if disposed in a suitable frame, can alsobe used to provide an indication of whether or not a surface isvertical.

However, such spirit levels are not capable of measuring deviations fromhorizontal or vertical outside a very limited range. Also, such spiritlevels can be difficult to read accurately as the measurement of levelor plumb depends on the ability of the user to determine the position ofthe bubble. Factors such as poor lighting or poor eyesight obviouslyaffect this.

Electronic spirit levels have been proposed, for example by Cantarella,in U.S. Pat. No. 4,167,818, which uses a capsule part-filled with aconductive liquid. Several electrodes are disposed within the capsule,the resistance between the electrodes being dependent on the position ofthe liquid within the capsule which, in turn, is dependent upon itsinclination. A digital readout of angles of inclination from level andfrom plumb is provided. However such levels suffer the disadvantage thatthe accuracy of any measurement from horizontal or vertical is dependentupon ambient conditions such as temperature, as fluctuations intemperature will lead to variations in the level and resistance ofliquid within the capsule which in turn will affect the reading ofinclination for angles for which the electrodes are not equally immersedin the liquid.

According to the invention in a first aspect there is provided acapsule, part filled with a liquid, the volume of the liquid varying asa function of temperature and the capsule being elastically deformablein response to temperature-induced pressure change within the capsule,so that the internal volume of the capsule is variable in dependenceupon temperature and whereby dimensions and material of walls of thecapsule are selected to provide a predetermined relationship between thelevel of liquid within the capsule and temperature.

According to the invention, in a second aspect there is provided acapsule, part-filled with a liquid, the walls or the capsule beingformed so that a temperature-induced pressure change within the capsulewill cause the walls of the capsule to deform elastically to maintainthe level of the liquid in the capsule substantially constant.

In the described embodiment of the invention a cylindrical capsule isprovided, the bulging of the radial walls of the capsule in response toincreased pressure within the capsule being chosen, by selecting thethickness and material for the radial walls, so that temperature inducedincrease in volume of the liquid is compensated by increased volume ofthe capsule, brought about by the change in configuration of the capsuleradial walls, to maintain the liquid level substantially constant.

Alternatively, the change in configuration of the capsule radial wallsis selected so that the liquid level fluctuates with temperature in apredetermined way.

In a particular application described, the capsule is used in aninclination measuring device in which measured resistances betweenelectrodes disposed in the capsule and the liquid are dependent oninclination and prone to fluctuation with temperature, due to changes inliquid level within the capsule and also due to fluctuations in theresistance of switches connected to the electrodes in relation to theresistance of the liquid. The fluctuations due to liquid level may becompensated for by adjusting the volume of the capsule in the mannermentioned above. However, by allowing the volume of the capsule tochange in a predetermined way which allows the level to fluctuate in apredicted manner, the temperature dependence of the resistance of theswitches and liquid may be compensated for together with compensationfor the change in liquid level, at least to a "best fit" approximation.

According to the invention in a third aspect there is provided a methodof calibrating in inclination sensor of the form comprising a capsulepart filled with a liquid, the position of the liquid within the capsulebeing indicative of the angle of rotation of the capsule about areference axis, a plurality of electrodes disposed within the capsulefor sensing said position within an angular range, an excitation source,a sensing circuit and means for connecting said electrodes to thesensing circuit and to the excitation source allow measurement of aplurality of electrical characteristics of the liquid which together areindicative of said position, said method comprising the steps of placingthe sensor at at least two known angles θ, measuring the correspondingsensed angles θ' and calculating from the known and sensed anglescalibration values a and b where;

    θ=aθ'+b

An embodiment of the invention will now be described, by way of example,with reference to the accompanying drawings, in which:

FIG. 1 is a perspective view of a sensor capsule forming part of anembodiment of the invention;

FIG. 2 is a sectional view taken in the plane II-II' of FIG. 1;

FIG. 3 is an exploded sectional view taken through the plane III-III' ofFIG. 1;

FIGS. 4A-B are sectional views similar to FIG. 2 of the capsule atdifferent inclinations;

FIG. 5 illustrates the angular range of the sensor.

FIG. 6 is a diagram for explaining the effect of change in liquid levelon capsule sensitivity.

FIG. 7 illustrates the ability of the capsule shown in FIGS. 1 to 3 tocompensate for temperature fluctuations.

FIGS. 8 and 9 are diagrams illustrating features of the designcalculations for calculating a preferred capsule wall thickness, fortemperature compensation purposes.

FIG. 10 is a diagram for explaining the effect of switch resistance oncapsule sensitivity.

Referring to FIGS. 1 to 3, an inclination sensor, generally designated 1is shown. The sensor comprises a capsule 3 of generally cylindricalform. The capsule 3 is formed from two engageable non-conductivechemically inert plastics mouldings 5,7 formed preferably fromthermoplastic polyester (e.g. a polybutylene terephthalate (PBT) forexample VALOX) reinforced with 15-20% glass beads to provide strengthand stability.

The mouldings 5, 7 are ultra-sonically welded together to ensure ahermetic seal. The end faces 9,11 of the mouldings 5,7 are formed of athickness so as to be elastically deformable in response to pressurevariations within the capsule 3, as described hereinafter.

Within mouldings 5,7, electrodes A,B and C,D formed from nickel arerespectively disposed. Each electrode A-D is of generally semi-circularform and is formed on its respective moulding 5,7 preferably by vacuumdeposition or hot foil blocking (although it is to be appreciated thatother electrode-forming methods may be employed). The electrodes A,B (orC,D) are separated one from the other by an elongate gap 8 (or 10) sothat the electrodes A,B or C,D are not in direct electrical contact. Thegaps 8,10 should be narrow, preferably less than 0.5 mm. Connections tothe electrodes A-D are provided by means of rivets formed fromconductive plastics material, which are bonded, preferably byultra-sonically welding to the case halves; rivets 13,15 for electrodesA,B are shown in FIG. 2.

Alternatively, the capsule may be formed from two identical plasticsdiscs, the electrodes being formed on the discs by silk screen printing,each disc then being connected to an open axial end of a hollowcylindrical plastics spacer, to form the capsule, the discs beingrotated by 90° relative to one another to give the desired electrodeconfiguration shown in FIG. 1.

The electrodes A,B are rotated by 90° about a reference axis O of thecapsule with respect to the electrodes C,D to allow measurement ofangles through 360° as described hereinafter. A conductive liquid 17 isdisposed within the capsule 3, preferably a mixture of distilled waterand methanol and a salt, for example sodium acetate trihydrate (CH₃COONa 3H₂ O), the capsule 3 being filled, at NTP to half its volume. Theremainder of the capsule is filled with air or an inert gas, for exampleargon.

The general mode of operation of the capsule is described with referenceto FIGS. 4A and 4B for which a measurement using electrodes A, B as thesensing electrodes is illustrated. FIGS. 4A and 4B illustrate thecapsule 3 in a schematically shown mounting 19 having an edge 21 whichis presented to a surface, the inclination of which is to be measured.One pair of electrodes in this case C, D are coupled together to form acommon electrode and an alternating voltage is applied in turn to theelectrodes A or B. The impedance and, more particularly, the resistanceof the path between electrodes C, D and electrode A or electrode B isdependent upon the degree of immersion of electrode A or electrode B inthe conductive liquid 17, the larger degree of immersion, the lower theresistance of the path.

Thus by measuring the resistances of the two paths, between electrodesC, D and electrode A and electrodes C, D and electrode B, the angle ofinclination θ of the sensor can be calculated.

More specifically as can be seen by comparison of FIGS. 4A and 4B, thetotal wetted area of electrodes A, B is always substantially a constant,so that, ignoring cross impedances: ##EQU1## where ^(Z) T=The totalresistance of the capsule

^(Z) 1=The resistance of the path CD to A

^(Z) 2=The resistance of the path CD to B ##EQU2##

So, the ratio, R, of the resistances Z1, Z2 is: ##EQU3##

Exemplary values of R are as follows:

                  TABLE 1                                                         ______________________________________                                                θ                                                                            ##STR1##                                                         ______________________________________                                               -90  ∞                                                                  -50  3.5                                                                      -45  3                                                                          0  1                                                                        +45  0.33                                                                     +50  0.286                                                                     90  0                                                                 ______________________________________                                    

Electrodes A, B are used for sensing angles up to ±50° from thehorizontal in the configuration illustrated in FIGS. 4A and 4B. Forangles of inclination greater than these limits, the electrodes may bereconfigured so that the electrodes A, B become the common electrode andthe orthogonally disposed electrodes C, D become the sensing electrodes,the sensor measuring angles in this configuration in the range ±50° fromvertical.

Reconfiguring the electrodes may conveniently be performed using aswitch matrix comprising a plurality of analogue switches, forconnecting each electrode to an alternating voltage source or to sensingcircuitry in common with another electrode, as appropriate.

Use of such electrode switching allows a full 360° of inclination angleto be measured, in terms of deviation from level or plumb, (as shown inFIG. 5) with the electrode configuration being chosen by computing andcontrol circuitry (not shown) in accordance with the angle ofinclination of the sensor. When initialising an inclination measurement,the control circuitry may perform a measurement with an arbitrary pairof electrodes e.g. C, D chosen as the common pair. If the ratio Rcalculated by the computing circuitry is within an allowable range (±50°) (see Table 1), the measurement proceeds whereas if the measured ratiois outside the allowable range, the configuration is changed to connectthe other pair of electrodes in common, and the measurement is thenperformed.

In the described capsule, the volume of the liquid 17 within the capsule3 is prone to fluctuation with temperature. Due to volume changesarising from differing thermal expansion of the capsule and the liquid,changes in temperature will result in changes in liquid level which willaffect the measurement of inclination. This effect is shown withreference to FIG. 6.

Assuming an increase in liquid level, in response to temperature, isindicated by change in height x.

Then, let S_(T) be the `total` conductivity of the half filled capsule:##EQU4## where Z_(A) ', Z_(B) ' are the resistances of paths CD to A andCD to B. ##EQU5## where S_(A) =the conductance due to plate area Aimmersed in the liquid

S_(A') =the conductance due to plate area A' immersed in the liquid##EQU6##

Combining 6, 7 and 8 and rearranging gives: ##EQU7##

Hence a correction factor a is: ##EQU8##

Thus it can be seen that as x changes with temperature, the sensed anglewill correspondingly change.

It can also be seen that if the capsule is not initially filled toexactly half its volume, an error which is dependent upon the consequentinitial difference in liquid level will result, independently of anytemperature induced change in liquid level. This may, however, becompensated for by calibration as described below.

In order to compensate for the change in level due to temperature, thesides 9, 11 of the capsule moulding 5, 7 are chosen to be of a thicknessso as to be elastically deformable in response to change in pressurecaused by change in volume of the liquid and change in gas vapourpressure within capsule 3 due to change in temperature as illustrated inFIG. 7 (for an increase in temperature). For a certain side thickness,the deformation of the sides 5, 7 will increase the volume of capsule 3to match the increased volume of the liquid so as to keep the level ofliquid 17 substantially constant, as illustrated by the followingexemplary design calculations:

ASSUMPTIONS

1) That it is necessary to prevent (or reduce to negligible proportions)the variation in liquid level with temperature, within an hermeticallysealed, part-filled, cylindrical vessel. (NB. the principle may beextended to non-cylindrical vessels).

2) That the liquid has a bulk coefficient of thermal expansion which ispositive, and significantly greater than that of the vessel.

3) That the gas or vapour filling the remainder of the vessel displays athermal variation of pressure which is essentially linear over theworking temperature range.

4) That the vessel material is homogeneous, isotropic and has a single,positive value of thermal expansivity. (NB. The principle may still beemployed if this assumption is not met, but the design calculationswould become more involved).

5) For this particular design, the cylindrical vessel is mounted withthe axis horizontal. The vessel walls are thin in relation to the vesselsize and are not stressed beyond the elastic limit. All deflections aresmall.

6) The cylindrical vessel has a diameter D=50 mm and an axial lengthL=10 mm

DESIGN CALCULATIONS

1) Differential thermal expansion

Consider a cylindrical vessel of diameter D, of unit axial length andfilled to a diameter with liquid of bulk thermal expansion coefficiente_(f). The vessel is made of material having a linear expansioncoefficient of e_(v), as illustrated in FIG. 8.

The linear expansion coefficient is defined such that at temperatureT+δT,

    diameter=D(1+e.sub.v δT)

and the bulk coefficient of the liquid similarly:

    volume=V(1+e.sub.f δT)

where V=initial volume at temperature T.

Now vessel volume at T ##EQU9## 2) Vessel bulging due to internalpressure For a flat circular plate, simply-supported at thecircumference, the deflection at any point at radius r from the centre,is given by: ##EQU10##

(REF ROARK. Formulas for stress and strain (McGraw Hill, 4th Edition)Page 216, Case 1)

where

P=internal pressure

a=radius of plate

E=Youngs modulus of plate material

t=plate thickness

v=poissons ration of plate material (assumes material is isotropic)

The incremental volume due to this deflection is given by: ##EQU11##

Assuming that pressure/temperature is given by the gas laws: ##EQU12##

Substituting values: ##EQU13##

3) Equate thermal expansion to vessel bulging. Taking expansivity valuesof exemplary materials used:

For methanol: e_(f) =1190 .10⁻⁶ (BULK)

For VALOX: e_(v) =70 .10⁻⁶ (LINEAR) (nominal value) ##EQU14##

The calculations assume that there is negligible pressure bulging of thecylindrical wall of the vessel and that both circular walls are of equalthickness.

The principle can still be employed if these assumptions are not met.

For ease of calculation, it has been assumed that the capsule walls aresimply-supported at the circumference and of uniform thickness. Morerefined analysis may be carried out within the ability of one skilled inthe art by, for example, finite element techniques to provide a moreaccurate determination of equation 14 for a particular application.

It is to be appreciated that this principle is usable in applicationsother than for the inclination sensor described.

The above compensation technique may be further employed to give addedtemperature compensation for other elements in the inclination sensor.More particularly, if the sensor is used to measure angles outside therange of electrodes AB by employing electrode switching to measure, forexample, a full 360° of inclination angle as previously described, ifelectronic switches to perform the electrode switching formed as part ofan application specific integrated circuit (ASIC), for example, are usedfor such switching, then the resistance of the switches will tend tochange with temperature.

Such resistance contributes to the total resistance of the sensor asmeasured, and thus the computing and control circuitry needs to becalibrated to take the switch resistance into account (as describedbelow). Such calibration cannot, however, compensate fortemperature-induced resistance fluctuation, without the use of atemperature sensor and a sizable increase in calibration memorycapacity.

The effect of switch resistance on measured angle will be illustratedwith reference to FIG. 10. For any usable electrode configuration, ananalogue switch having a resistance r_(sw) will be connected to eachelectrode, thus modifying the total sensed resistance ratio (R) of thecapsule as follows: ##EQU15##

As θ and θ' have the same sign, and since α < < 1, using a Taylorexpansion: ##EQU16##

The term ##EQU17## is dependent upon temperature due to fluctuation inr_(sw) as mentioned above and also due to fluctuation in total capsuleresistance Z_(T). However it can be seen that the totalangular-dependent compensation factor a' for liquid level and for switchresistance is: ##EQU18##

As previously discussed, the capsule can be designed to deform, to that##EQU19## remains constant. However, the capsule can further be made todeform to compensate, to some extent for changes in ##EQU20## so thatthe temperature dependence of the compensation factor a' is reducedstill further. In this case, the level of liquid in the capsule willfluctuate slightly with temperature in order to provide the additionalcompensation for the switch and liquid resistance change.

For example, the compensation factor a' may be rewritten in temperaturedependent form as: ##EQU21## where ΔT represents a change in temperaturefrom the measured values of r_(sw) and Z_(T) at a given temperature (20°in this example) and χ is the temperature dependent change in liquidlevel in mm/K.

For perfect temperature compensation: ##EQU22##

α and β may be found by experimentation so that the desired value for χmay be calculated and the capsule geometry designed to provide thenecessary compensation for the non-zero height change χ, in a similarmanner to that described with reference to equations 11 to 16.

In general, the capsule can be designed to deform in response totemperature to maintain the electrical transfer function of the capsuleand any external sensor circuitry independent of temperature or at leastto provide a "best fit" over a desired temperature range. In such acase, the temperature dependence of a capsule could be establishedempirically and the capsule design modified to provide the most usefulcompensation, in the manner previously described.

As described above, initial conditions (independent of temperatureinduced change) exist in the capsule and sensor, and the capsule andsensor need to be calibrated to take these initial conditions intoaccount.

In general, the angle sensed by the capsule described above andassociated sensor circuitry (θ') is related to the actual angle ofinclination (θ) by the following expression: ##EQU23## The calibrationfactors a* and b are dependent, to some extent, on the position of theelectrodes within the capsule and any errors in the placement of theelectrodes will result in changes in the calibration factors, so thatdifferent factors a*, b usually exist for each pair of electrodes A, Bor C, D.

The inventors have found that the dominant influence affectingcalibration factor a* is related to the variation in initial liquidlevel with respect to the measuring electrodes which is linearly relatedto angle, as is apparent from equation 10. The coefficients C₂ -C_(N)are, consequently, small in comparison to C₁ for capsules withreasonable manufacturing tolerances.

Thus, it can be seen from equation 26 that with this approximation theactual angle θ is a linear function of sensed angle θ'.

Thus, if θ is plotted against θ', the gradient of the resulting straightline will give a*. Thus, by placing the capsule at two, known angles θ₁,θ₂ measuring the corresponding sensed angles θ₁ ', θ₂ ' will providesufficient data for establishing the gradient of the straight linebetween these two points and so will give a*.

Then by applying the initial condition that θ=θ' at the origin (0°), bcan then be calculated as follows: ##EQU24##

As the calibration factor b is dependent upon the electrode-to-measuringsurface relationship, if the capsule is inverted, the sign of thecalibration parameter b needs to be changed to provide the appropriatecompensation.

At the manufacturing stage, the values of a* and b may be stored in aprogrammable read only memory (PROM) for use by the computing andcontrol circuitry when calculating the actual inclination angle.

When calculating a* for the capsule of FIG. 1, preferably the knownangles are chosen as ±45°. This difference in angles is chosen as itwill be appreciated that although the terms C₂ -C_(N) are small, they dohave some effect upon the measurement of angle. By choosing actualangles at opposed ends of the available angular range of the pair ofplates, and by forcing the resulting straight line graph through theorigin (θ=θ'=0 (equation 33)), a reasonable spread of calibrationcompensation is given over the whole sensing range.

It will be noted that electrode configuration of plates A, B (forexample) is usable to measure either 0° or 180°, depending upon whetherthe inclination measuring surface 21 is upside down or the right way up.In order to distinguish between these two conditions (or any otherequivalent condition) in which identical areas of electrodes A and B areimmersed in the liquid and where the difference in angular positiondepends upon the disposition of the surface 21, additional informationconcerning which of the two possible angles the inclination themeasuring device is inclined at may be obtained by measuring the sameangle for electrodes C and D. It can be seen that the position of theliquid relative to plates C and D will be different for the two"equivalent" inclinations measurable using plates A and B.

For the electrode arrangement as shown in the capsule of FIGS. 1 and 8the following relationship holds:

                  TABLE 3                                                         ______________________________________                                                                          Polarity of                                                                   Angular                                                                       Measurement                                                         Non       for Non                                     Measuring               Measuring Measuring                                   Electrodes                                                                            Range           Electrodes                                                                              Electrodes                                  ______________________________________                                        (i)  A,B    50° < θ < -50°                                                            C,D     -ve                                       (ii) A,B    θ > 130°; θ < -130°                                                 C,D     +ve                                       (iii)                                                                              C,D    -140° < θ < -40°                                                          A,B     -ve                                       (iv) C,D    40° < θ < 140°                                                            A,B     +ve                                       ______________________________________                                    

This relationship may then be used to enable the computing circuitry todecide whether or not the factor b should be added or subtracted.

We claim:
 1. A capsule, part filled with a liquid, the volume of theliquid varying as a function of temperature and the capsule beingelastically deformable in response to temperature-induced pressurechange within the capsule, so that the internal volume of the capsule isvariable in dependence upon temperature and whereby dimensions andmaterial of walls of the capsule are selected to provide (apredetermined relationship between the level of liquid within thecapsule and temperature) that the level of liquid remains substantiallyconstant with respect to temperature over a temperature range.
 2. Acapsule as claimed in claim 1 wherein the capsule is formed fromplastics material.
 3. A capsule as claimed in claim 2 wherein theplastics material is a polybutylene terephthalate.
 4. A capsule asclaimed in claim 2 wherein the plastics material is reinforced withglass beads.
 5. A capsule as claimed in claim 1 wherein the liquidincludes methanol.
 6. A capsule as claimed in claim 1, wherein thecapsule is formed as a hollow cylinder, the end walls of the cylinderbeing arranged to deform in response to said pressure change and thecylindrical side wall of the cylinder being arranged to be irresponsiveto said change.
 7. A capsule as claimed in claim 1 wherein the capsulecomprises first and second mouldings connected together.
 8. A capsule asclaimed in claim 6 wherein the capsule comprised a hollow cylindricalmember and first and second discs, each disc being connected to an endof the cylindrical member.
 9. An inclination sensor including a capsuleas claimed in claim 1 further comprising a plurality of electrodesconnected to the capsule for sensing an electrical characteristic acrossthe liquid said electrical characteristic varying in dependence upon theinclination of the capsule about a reference axis so that the sensor hasan electrical transfer function which is a function of inclinationangle.
 10. A sensor as claimed in claim 9 wherein said predeterminedrelationship is selected to provide compensation for the dependence ontemperature of said transfer function over a temperature range.
 11. Asensor as claimed in claim 9 further comprising switch means forconnecting the electrodes in a plurality of desired configurations, theswitch means having an electrical transfer function which is a functionof temperature.
 12. A sensor as claimed in claim 11 wherein saidpredetermined relationship is selected to provide compensation for thedependence on temperature of the combined electrical transfer functionof the capsule and switch means over a temperature range.
 13. A sensoras claimed in claim 9 wherein said plurality of electrodes includesfirst and second electrodes disposed within the capsule, the relativedegree of immersion of the first and second electrodes in the liquidbeing indicative, within a first angular range, of the angle ofinclination of the capsule both about the reference axis and relative toa first reference condition.
 14. A sensor as claimed in claim 13 whereinsaid plurality of electrodes further includes third and fourthelectrodes disposed within the capsule, the relative degree of immersionof the third and fourth electrodes in the liquid being indicative,within a second angular range, of the angle of inclination of thecapsule both about a reference axis and relative to a second referencecondition different from the first reference condition.
 15. A sensor asclaimed in claim 14 wherein the first and second reference conditionsare those at which the first and second electrodes or the third andfourth electrodes, respectively, are equally immersed in the liquid. 16.A sensor as claimed in claim 14 wherein the first to fourth electrodesare arranged so that any angle of inclination of the capsule about thereference axis is included within at least one of the first and secondranges.
 17. A sensor as claimed in claim 14 wherein the first and secondreference conditions are orthogonally disposed.
 18. A sensor as claimedin claim 13 wherein the first and second electrodes are of substantiallysemi-circular form and are spaced one from the other about the referenceaxis.
 19. A sensor as claimed in claim 14 wherein the third and fourthelectrodes are of semi-circular form and are spaced one from the otherabout the reference axis.
 20. An inclination measuring device includinga sensor as claimed in claim 13, the sensor being mounted relative to ameasuring surface disposed parallel to the first reference condition, sothat inclination of the measuring surface results in correspondinginclination of the sensor capsule.
 21. A capsule, part filled with aliquid, the walls of the capsule being formed so that atemperature-induced pressure change within the capsule will cause thewalls of the capsule to deform elastically to maintain the level of theliquid in the capsule substantially constant.
 22. A capsule as claimedin claim 21 wherein the capsule is formed from plastics material.
 23. Acapsule as claimed in claim 22 wherein the plastics material is apolybutylene terephthalate.
 24. A capsule as claimed in claim 22 whereinthe plastics material is reinforced with glass beads.
 25. A capsule asclaimed in claim 21 wherein the liquid comprises methanol.
 26. A capsuleas claimed in claim 21 wherein the capsule is formed as a hollowcylinder, the end walls of the cylinder being arranged to deform inresponse to said pressure change and the cylindrical side wall of thecylinder being arranged to be irresponsive to said change.
 27. A capsuleas claimed in claim 21 wherein the capsule comprises first and secondmouldings connected together.
 28. A capsule as claimed in claim 26wherein the capsule comprises a hollow cylindrical member and (bit)first and second discs, each disc being connected to a respective end ofthe cylindrical member.
 29. An inclination sensor including a capsule asclaimed in claim
 21. 30. A sensor as claimed in claim 29 wherein thecapsule further includes a plurality of electrodes arranged for contactwith the liquid.
 31. A sensor as claimed in claim 30 wherein saidplurality of electrodes includes first and second electrodes disposedwithin the capsule, the relative degree of immersion of the first andsecond electrodes in the liquid being indicative, within a first angularrange, of the angle of inclination of the capsule both about a referenceaxis and relative to a first reference condition.
 32. A sensor asclaimed in claim 31 wherein said plurality of electrodes furtherincludes third and fourth electrodes disposed within the capsule, therelative degree of immersion of the third and fourth electrodes in theliquid being indicative, within a second angular range, of the angle ofinclination of the capsule both about a reference axis and relative to asecond reference condition different from the first reference condition.33. A sensor as claimed in claim 32 wherein the first and secondreference conditions are those at which the first and second electrodesor the third and fourth electrodes, respectively, are equally immersedin the liquid.
 34. A sensor as claimed in claim 31 wherein the first tofourth electrodes are arranged so that any angle of inclination of thecapsule about the reference axis is included within at least one of thefirst and second ranges.
 35. A sensor as claimed in claim 32 wherein thefirst and second reference conditions are orthogonally disposed.
 36. Asensor as claimed in claim 31 wherein the first and second electrodesare of substantially semi-circular form and are spaced one from theother about the reference axis.
 37. A sensor as claimed in claim 32wherein the third and fourth electrodes are of semi-circular form andare spaced one from the other about the reference axis.
 38. Aninclination measuring device including a sensor as claimed in claim 31,the sensor being mounted relative to a measuring surface disposedparallel to the first reference condition, so that inclination of themeasuring surface results in corresponding inclination of the sensorcapsule.
 39. A method of calibrating an inclination sensor of the formcomprising a capsule part filled with a liquid, the position of theliquid within the capsule being indicative of the angle of rotation ofthe capsule about a reference axis, a plurality of electrodes disposedwithin the capsule for sensing said position within an angular range, anexcitation source, a sensing circuit and means for connecting saidelectrodes to the sensing circuit and to the excitation source allowmeasurement of a plurality of electrical characteristics of the liquidwhich together are indicative of said position, said method comprisingthe steps of placing the sensor at least two known angles θ, measuringthe corresponding sensed angles θ' and calculating from the known andsensed angles calibration values a and b where:

    θ=aθ'+b


40. A method as claimed in claim 39 wherein a is taken to be constantwithin at least one part of said angular range.
 41. A method as claimedin claim 40 wherein b is taken to be equal to -a θ' at θ=0.
 42. A methodas claimed in claim 39 wherein the sensor includes a first pair ofelectrodes arranged to measure angles within a first said part of saidangular range and a second pair of electrodes arranged to measure angleswithin a second said part of said angular range.
 43. A method as claimedin claim 42 wherein said first part comprises a range of angles α andsaid first pair of electrodes are arranged to measure angles within afurther part of said range, which comprises a range of angles 180°+α andwhen in said further part, the said factor b is taken to be equivalentin magnitude but of opposite sign to the factor b of said first part.44. A method as claimed in claim 42 wherein said second part comprises arange of angles β and said second pair of electrodes are arranged tomeasure angles within a further range of angles 180°+β and when in saidfurther part, the said factor b is taken to be equivalent in magnitudebut of opposite sign to the factor b of said second part.